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Exchange rate volatility and the mixture of distribution hypothesis 27
Appendix: Data sources and transformations
The data transformations were undertaken in Ox 3.4 and EViews 5.1.
Sn(t) n(t)=1(t), 2(t),.., N(t), where S1(t) is the first BID NOK/1EUR opening exchange rate of
week t, S2(t) is the first closing rate, S3(t) is the second opening rate, and so on, with SN(t)
denoting the last closing rate of week t. Before 1.1.1999 the BID NOK/1EUR rate is
obtained by the formula BID NOK/100DEM×0.0195583, where 0.0195583 is the official
DEM/1EUR conversion rate 1.95583 DEM=1 EUR divided by 100. The first untransformed
observation is the opening value of BID NOK/100DEM on Wednesday 6.1.1993
and the last is the BID NOK/1EUR closing value on Friday 26.12.2003. The source of the
BID NOK/100DEM series is Olsen and the source of the BID NOK/1EUR series is Reuters.
St SN(t), the last closing value of week t
rt log St−log St−1
Vt w {{log[St+I(St=St−1)×0.0009]−log(St−1)} ×100} 2 . I(St=St−1) is an indicator function equal to
1ifSt=St−1 and 0 otherwise, and St=St−1 occurs for t=10/6/1994, t=19/8/1994 and
t=17/2/2000.
vt w
log Vt w
Vt r Σn [log(Sn/Sn−1)×100] 2 , where n=1(t), 2(t),..., N(t) and 1(t)−1≔N(t−1)
vt r
log Vt r
Mn(t) n(t)=1(t), 2(t),.., N(t), where M1(t) is the first BID USD/EUR opening exchange rate of
week t, M2(t) is the first closing rate, M3(t) is the second opening rate, and so on, with MN(t)
denoting the last closing rate of week t. Before 1.1.1999 the BID USD/EUR rate is obtained
with the formula 1.95583/(BID DEM/USD). The first untransformed observation is the
opening value of BID DEM/USD on Wednesday 6.1.1993 and the last is the closing value
on Friday 30.12.2003. The source of the BID DEM/USD and BID USD/EUR series is
Reuters.
Mt MN(t), the last closing value of week t
mt log Mt
Mt w {{log[Mt+I(Mt=Mt-1)×kt]−log(Mt-1)}×100} 2 . I(Mt=Mt−1) is an indicator function equal to 1
if Mt=Mt−1 and 0 otherwise, and kt is a positive number that ensures the log-transformation
is not performed on a zero-value. Mt=Mt−1 occurs for t=23/2/1996, t=19/12/1997 and
t=20/2/1998, and the value of kt was set on a case to case basis depending on the number of
decimals in the original, untransformed data series. Specifically the values of kt were set to
0.00009, 0.0009 and 0.00009, respectively.
mt w log Mt w
Mt r Σn [log(Mn/Mn−1)×100] 2 , where n =1(t), 2(t),.., N(t) and 1(t)−1≔N(t−1)
mt r
log Mt r
Qt Weekly number of NOK/EUR quotes (NOK/100DEM before 1.1.1999). The underlying
data is a daily series from Olsen Financial Technologies, and the weekly values are obtained
by summing the values of the week.
qt log Qt. Note that this series is “synthetic” in that it has been adjusted for changes in the
underlying quote-collection methodology at Olsen Financial Technologies. More precisely
qt has been generated under the assumption that Δqt was equal to zero in the weeks
containing Friday 17 August 2001 and Friday 5 September 2003, respectively. In the first
week the underlying feed was changed from Reuters to Tenfore, and on the second a feed
from Oanda was added.
On(t) n(t)=2(t), 4(t),.., N(t), where O2(t) is the first closing value of the Brent Blend spot oilprice in
USD per barrel in week t, O4(t) is the second closing value of week t, and so on, with On(t)
denoting the last closing value of week t. The untransformed series is Bank of Norway
database series D2001712, which is based on Telerate page 8891 at 16.00.
Ot ON(t), the last closing value in week t
ot
log Ot
Ot w {log[Ot+I(Ot=Ot−1)×0.009]−log(Ot−1) } 2 . I(Ot=Ot−1) is an indicator function equal to 1 if
Ot=Ot−1 and 0 otherwise, and Ot=Ot−1 occurs three times, for t=1/7/1994, t=13/10/1995 and
t=25/7/1997.